Python: Merge sort

Last update on April 23 2025 12:56:58 (UTC/GMT +8 hours)

8. Merge Sort

Write a Python program to sort a list of elements using the merge sort algorithm.
Note: According to Wikipedia "Merge sort (also commonly spelled mergesort) is an O (n log n) comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output."

Algorithm:

Conceptually, a merge sort works as follows :

Divide the unsorted list into n sublists, each containing 1 element (a list of 1 element is considered sorted).
Repeatedly merge sublists to produce new sorted sublists until there is only 1 sublist remaining. This will be the sorted list.

An example of merge sort:

Merge Sort animation

Merge Sort: Pictorial Presentation

Pictorial Presentation: Merge sort

Sample Solution:

Python Code:

def mergeSort(nlist):
    print("Splitting ",nlist)
    if len(nlist)>1:
        mid = len(nlist)//2
        lefthalf = nlist[:mid]
        righthalf = nlist[mid:]

        mergeSort(lefthalf)
        mergeSort(righthalf)
        i=j=k=0       
        while i < len(lefthalf) and j < len(righthalf):
            if lefthalf[i] < righthalf[j]:
                nlist[k]=lefthalf[i]
                i=i+1
            else:
                nlist[k]=righthalf[j]
                j=j+1
            k=k+1

        while i < len(lefthalf):
            nlist[k]=lefthalf[i]
            i=i+1
            k=k+1

        while j < len(righthalf):
            nlist[k]=righthalf[j]
            j=j+1
            k=k+1
    print("Merging ",nlist)

nlist = [14,46,43,27,57,41,45,21,70]
mergeSort(nlist)
print(nlist)

Sample Output:

Splitting  [14, 46, 43, 27, 57, 41, 45, 21, 70]                                                               
Splitting  [14, 46, 43, 27]                                                                                   
Splitting  [14, 46]                                                                                           
Splitting  [14]                                                                                               
Merging  [14]                                                                                                 
Splitting  [46]                         
-------
Merging  [14, 21, 27, 41, 43, 45, 46, 57, 70]                                                                 
[14, 21, 27, 41, 43, 45, 46, 57, 70]

Flowchart:

For more Practice: Solve these Related Problems:

Write a Python program to implement merge sort and print the sublists at each merge step.
Write a Python script to sort a list using merge sort and count the total number of comparisons made during the merge process.
Write a Python program to apply merge sort on a list of dictionaries based on a specific key.
Write a Python function to perform merge sort recursively and then verify its stability on a list with duplicate values.

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